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Quantum Cryptography

December, 3 rd 2007 Philippe LABOUCHERE Annika BEHRENS. Quantum Cryptography. Introduction Photon sources Quantum Secret Sharing. Introduction Photon sources Quantum Secret Sharing. How to measure information (1). Claude E. Shannon 1948 Information entropy Mutual information. [bits].

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Quantum Cryptography

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  1. December, 3rd 2007 Philippe LABOUCHERE Annika BEHRENS Quantum Cryptography

  2. Introduction • Photon sources • Quantum Secret Sharing

  3. Introduction • Photon sources • Quantum Secret Sharing

  4. How to measure information (1) • Claude E. Shannon 1948 • Information entropy • Mutual information [bits]

  5. How to measure information (2) • Relation between H and I • Mutual information between 2 parties

  6. Venn diagrams

  7. The BB84 protocol

  8. The BB84 protocol: principle • 2 conjugate basis • Information encoded in photon’s polarization → ’0’ ≡ —& / → ’1’ ≡ | & \ • Quantum & classical channels used for key exchange Charles H. Bennett Gilles Brassard

  9. From random bits to a sifted key Quantum transmission Public discussion

  10. Mutual information vs quantum bit error rate

  11. The no-cloning theorem • Dieks, Wootters, Žurek 1982 ”It is forbidden to create identical copies of an arbitrary unknown quantum state.” • Quantum operations : unitary & linear transformations on the state of a quantum system

  12. Introduction • Photon sources • Quantum Secret Sharing

  13. Sources of photons • Thermal light • Coherent light • Squeezed light Average photon number of photons in a mode Number of photons

  14. Faint-laser pulses • <n> = μ~ 0.1 photon / pulse • Photon-number splitting attack! • Dark counts of detectors vs high pulse rate & weaker pulses Detection yield Transmission efficiency ! Tradeoff

  15. Entangled photon pairs • Spontaneous Parametric Down Conversion • Idler photon acts as trigger for signal photon • Very inefficient

  16. Single-photon sources • Intercept/resend attack => error rate < dark count rate ! • Condition for security: • Drawback : dark counts & afterpulses Detection yield Transmission efficiency

  17. Practical limits of QC • Realization of signal • Stability under the influence of the environment (transportation) - Birefringence - Polarization dispersion - Scattering • Need of efficient sources & detectors (measurements)

  18. Bite rate as function of distance after error correction and privacy amplification Pulse rate = 10 MHz μ = 0.1 (faint laser pulses) Losses:@ 800nm : 2dB / km @ 1300 nm: 0.35dB / km @ 1550 nm: 0.25 dB /km

  19. Introduction • Photon sources • Quantum Secret Sharing

  20. Quantum Secret Sharing (1)

  21. QSS (2) • N-qubit GHZ source • Define

  22. Goodbye GHZ, welcome single qubit

  23. Sequentially polarized single photon protocol

  24. Questions ?

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